A completeness theorem for a dissipative Schrodinger problem with the spectral parameter in the boundary condition


ONGUN M. Y. , Allahverdiev B.

MATHEMATISCHE NACHRICHTEN, cilt.281, sa.4, ss.541-554, 2008 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 281 Konu: 4
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1002/mana.200410623
  • Dergi Adı: MATHEMATISCHE NACHRICHTEN
  • Sayfa Sayıları: ss.541-554

Özet

In this paper we consider a dissipative Schrodinger boundary value problem in the limit-circle case with the spectral parameter in the boundary condition. The approach is based on the use of the maximal dissipative operator, and the spectral analyzes of this operator is adequate for the boundary value problem to be solved. We construct a self-adjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We also construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrodinger equation. We prove theorems on the completeness of the system of eigenvectors and associated vectors of the maximal dissipative operator and the Schrodinger boundary value problem. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.